At a point P, the electric field is 78 N/C at 51° counter-clockwise from the positive x axis. A particle of mass 4.7 kg and charge -0.11 C is located at P. Find
the direction of the force on the particle: ___ degrees counter-clockwise from the positive x axis
the direction of the acceleration of the particle: ___ degrees counter-clockwise from the positive x axis
I don't understand this
To find the direction of the force on the particle, we can use the formula for the force experienced by a charged particle in an electric field:
F = qE
Where:
F is the force
q is the charge of the particle
E is the electric field
Given:
q = -0.11 C
E = 78 N/C
Since the electric field is given as a vector with a magnitude and direction, we need to decompose it into its x and y components. We can use trigonometry to find the components:
E_x = E * cos(θ)
E_y = E * sin(θ)
Where:
θ is the angle of the electric field, measured counter-clockwise from the positive x-axis.
Given:
E = 78 N/C
θ = 51 degrees
Calculating the x and y components:
E_x = 78 N/C * cos(51 degrees)
E_y = 78 N/C * sin(51 degrees)
E_x ≈ 49.929 N/C
E_y ≈ 59.910 N/C
Now, we can use the force formula:
F = qE
F_x = q * E_x
F_y = q * E_y
Substituting the values:
F_x = -0.11 C * 49.929 N/C
F_y = -0.11 C * 59.910 N/C
F_x ≈ -5.492 N
F_y ≈ -6.590 N
The force components are F_x ≈ -5.492 N and F_y ≈ -6.590 N.
To find the direction of the force on the particle, we can use the inverse tangent function:
θ_force = atan(F_y / F_x)
θ_force ≈ atan(-6.590 N / -5.492 N)
θ_force ≈ atan(1.198)
θ_force ≈ 49.5 degrees
So, the direction of the force on the particle is approximately 49.5 degrees counter-clockwise from the positive x-axis.
To find the direction of the acceleration of the particle, we need to consider Newton's second law:
F = m * a
Where:
F is the force
m is the mass of the particle
a is the acceleration
Given:
F_x ≈ -5.492 N
F_y ≈ -6.590 N
m = 4.7 kg
To find the acceleration components, we can rearrange the equation:
a_x = F_x / m
a_y = F_y / m
Substituting the values:
a_x = -5.492 N / 4.7 kg
a_y = -6.590 N / 4.7 kg
a_x ≈ -1.169 m/s^2
a_y ≈ -1.398 m/s^2
Now, we can use the inverse tangent function to find the direction of the acceleration:
θ_acceleration = atan(a_y / a_x)
θ_acceleration ≈ atan(-1.398 m/s^2 / -1.169 m/s^2)
θ_acceleration ≈ atan(1.195)
θ_acceleration ≈ 48.8 degrees
So, the direction of the acceleration of the particle is approximately 48.8 degrees counter-clockwise from the positive x-axis.
To find the direction of the force on the particle, we can use the relationship between the electric field and the force experienced by a charged particle. The force experienced by a charged particle is given by the equation:
F = q * E
where F is the force, q is the charge of the particle, and E is the electric field. In this case, the charge of the particle is -0.11 C and the electric field is given as 78 N/C.
Since the charge of the particle is negative, the force will be in the opposite direction of the electric field. The direction of the electric field is given as 51° counter-clockwise from the positive x-axis. Therefore, the direction of the force on the particle will be 51° clockwise from the positive x-axis.
To find the direction of the acceleration of the particle, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The equation is:
F = m * a
where F is the force, m is the mass of the particle, and a is the acceleration.
In this case, the mass of the particle is given as 4.7 kg and the force is calculated in the previous step as -0.11 C * 78 N/C.
Since the force is negative, the acceleration will also be in the opposite direction. Therefore, the direction of the acceleration of the particle will be 51° clockwise from the positive x-axis.